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Smooth implicit surfaces, also known as metaballs or soft 
objects, form the second layer [Blinn, 1982]. They are 
used to simulate the gross behavior of bone, muscle, and 
fat tissue. The metaballs are attached to the skeleton and 
arranged in an anatomically-based approximation. Head, 
hands and feet are explicit surfaces that are attached to 
the body. For display purposes a third layer, a polygonal 
skin surface, is constructed by ray casting [Thalmann et al., 
1996]. 
The body shape and position are controlled by a state vec- 
tor O, which is a set of parameters controlling joint loca- 
tions and limb sizes. In this section, we first describe this 
state vector in more detail and, then, our implicit surface 
formulation. 
2. State Vector 
Our goal is to use video-sequences to estimate our model's 
shape and derive its position in each frame. Let us there- 
fore assume that we are given N consecutive video frames 
and introduce position parameters for each frame. 
Let B be the number of body parts in our model. We assign 
to each body part a variable length and width coefficient. 
These dimensions change from person to person but we 
take them to be constant within a particular sequence. This 
constraint could be relaxed, for example to model muscular 
contraction. 
The model's shape and position are then described by the 
combined state vector 
oz (0,0, 97,07, (1) 
  
  
(f) 
Figure 1: Models and silhouettes. (a) Metaballs attached to an articulated skeleton. (b) Skin surface computed by ray casting. 
(c) One image of a stereo pair used to estimate the parameters of the model in (b). (d) Corresponding disparity map. 
(e) The real body outlines overlaid on the skin surface. In this case the model was fitted using stereo only. As a result, 
it ends up too far from the actual data points and the system compensates by incorrectly enlarging the primitives. (f) 
Using the silhouettes during the fitting process provides stricter constraints that yield a better result. 
where O is broken into sub-vectors that control the follow- 
ing model components: 
e Shape 
— Q" — (8? | b — 1..B), the width of body parts. 
— 9! « (8! | b — 1..B), the length of body parts. 
e Motion 
- 6 = (6, | j = LAf = 1..N}, the rotational 
degree of freedom of joint j of the articulated 
skeleton for all frames f 
- 99 z (09 | f = 1.N}, the six parameters of 
global position and orientation of the model in 
the world frame for all frames f 
The size and position of the metaballs is relative to the seg- 
ment they are attached to. A length parameter not only 
specifies the length of a skeleton segment but also the shape 
of the attached metaballs in the direction of the segment. 
Width parameters only influence the metaballs’ shape in 
the other directions. 
2.2 Metaballs 
Metaballs [Blinn, 1982] are generalized algebraic surfaces 
that are defined by a summation over n 3-dimensional Gaus- 
sian density distributions, each called a primitive. The final 
surface S is found where the density function F equals a 
threshold T', taken to be 0.5 in this work: 
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RE SET 
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